| Euclides - 1826 - 226 pages
...parallelograms having equal bases, are to each other as their altitudes. PROPOSITION II. THEOREM. У a right **line be drawn parallel to one of the sides of a triangle, it** shall cut the sides of the triangle proportionally j and if the sides of a triangle be cut proportionally,... | |
| John Radford Young - Euclid's Elements - 1827 - 208 pages
...; but by hypothesis, A2 : B" :': A : C, hence (Prop. IX. Cor. 3. BV), Q=C. PROPOSITION V. THEOREM. **If a straight line be drawn parallel to one of the sides of a triangle, it** shall cut the other sides, or those produced, proportionally ; and conversely, if the sides or the... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...construction be made as in the pro, . - position, the demonstration will be the same. PROP. II. THEOR. 3ee N. **If a straight line be drawn parallel to one of the sides of a triangle, it** shall cut the other sides, or these produced, proportionally : and if the sides, or the sides produced,... | |
| John Radford Young - Euclid's Elements - 1827 - 246 pages
...triangle are respectively equal to those of another, the triangles are similar. Cor. 2. Therefore if a **line be drawn parallel to one of the sides of a triangle it will cut** off a triangle similar to the whole. PROPOSITION x. THEOREM. {Converse of Prop. IX.} The angles of... | |
| John Playfair - Geometry - 1829 - 186 pages
...BOOK VI. Triangles, and also parallelograms, of the same altitude are to one another as their bases. **If a straight line be drawn parallel to one of the sides of a triangle it will cut the other** two sides proportionally. If any angle of a triangle be bisected by a straight line which cuts the... | |
| Euclid, Robert Simson - Geometry - 1829 - 516 pages
...: then, if the same construction be made as in the proposition, the demonstration will be the same. **PROP. II. THEOR. IF a straight line be drawn parallel to one of the sides of a triangle, it** shall cut the other sides, or those produced, proportionally ; and if the sides, or the sides produced,... | |
| Euclides - 1834 - 518 pages
...construction be made aq in the proposition, the demonstration will be the same. PROPOSITION II. ^ See N. **THEOR. — If a straight line be drawn parallel to one of the sides of a triangle, it** shall cut the other sides, or these produced, proportionally : and if the tides, or the sides produced,... | |
| Euclid - 1835 - 540 pages
...another. Then, if the same construction be made as in the proposition, the demonstration will be the same. **PROP. II. THEOR. If a straight line be drawn parallel to one of the** See N. sides of a triangle, it will cut the other sides, or the other sides produced, proportionally... | |
| John Playfair - Geometry - 1836 - 114 pages
...base and altitude, therefore triangles of equal altitude are to one another as their bases. PROP. III. **THEOR. \ If a straight line be drawn parallel to one of the sides of a triangle, it** shall cut the other sides, or these produced, proportionally ; and if the sides, or the sides produced... | |
| Euclid - Geometry - 1837 - 410 pages
...triangle ADE ; and * The enunciation of this proposition, as given by Dr. Simson, is as follows : " **If a straight line be drawn parallel to one of the sides of a triangle, it** shall cut the other sides, or those produced, proportionally : and if the sides, or the sides produced,... | |
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